Asymptotic Statistical Inference: A Basic Course Using R

The book discusses asymptotic statistical inference theory, focusing on large sample optimality properties of estimators and test procedures. It covers consistent and asymptotically normal (CAN) estimators, likelihood ratio test procedures, and applications to multinomial distributions. It also discusses score tests and Walds tests, their relationship with the likelihood ratio test, and Karl Pearsons chi-square test. The book uses R software extensively to illustrate concepts, verify estimator properties, and carry out test procedures. It is designed as a text book for a one-semester introductory course in asymptotic statistical inference, and will also serve as a background for studying inference in stochastic processes.

Format: Hardback
Length: 529 pages
Publication date: 05 July 2021
Publisher: Springer Verlag, Singapore

The book presents the fundamental concepts from asymptotic statistical inference theory,elaborating on some basic large sample optimality properties of estimators and some test procedures. The most desirable property of consistency of an estimator and its large sample distribution,with suitable normalization,are discussed,the focus being on the consistent and asymptotically normal (CAN) estimators. It is shown that for the probability models belonging to an exponential family and a Cramer family,the maximum likelihood estimators of the indexing parameters are CAN. The book describes some large sample test procedures,in particular,the most frequently used likelihood ratio test procedure. Various applications of the likelihood ratio test procedure are addressed,when the underlying probability model is a multinomial distribution. These include tests for the goodness of fit and tests for contingency tables. The book also discusses a score test and Walds test,their relationship with the likelihood ratio test and Karl Pearsons chi-square test. An important finding is that,while testing any hypothesis about the parameters of a multinomial distribution,a score test statistic and Karl Pearsons chi-square test statistic are identical. Numerous illustrative examples of differing difficulty level are incorporated to clarify the concepts. For better assimilation of the notions,various exercises are included in each chapter. Solutions to almost all the exercises are given in the last chapter,to motivate students towards solving these exercises and to enable digestion of the underlying concepts.
The concepts from asymptotic inference are crucial in modern statistics,but are difficult to grasp in view of their abstract nature. To overcome this difficulty,keeping up w.

The book presents the fundamental concepts from asymptotic statistical inference theory,elaborating on some basic large sample optimality properties of estimators and some test procedures. The most desirable property of consistency of an estimator and its large sample distribution,with suitable normalization,are discussed,the focus being on the consistent and asymptotically normal (CAN) estimators. It is shown that for the probability models belonging to an exponential family and a Cramer family,the maximum likelihood estimators of the indexing parameters are CAN. The book describes some large sample test procedures,in particular,the most frequently used likelihood ratio test procedure. Various applications of the likelihood ratio test procedure are addressed,when the underlying probability model is a multinomial distribution. These include tests for the goodness of fit and tests for contingency tables. The book also discusses a score test and Walds test,their relationship with the likelihood ratio test and Karl Pearsons chi-square test. An important finding is that,while testing any hypothesis about the parameters of a multinomial distribution,a score test statistic and Karl Pearsons chi-square test statistic are identical. Numerous illustrative examples of differing difficulty level are incorporated to clarify the concepts. For better assimilation of the notions,various exercises are included in each chapter. Solutions to almost all the exercises are given in the last chapter,to motivate students towards solving these exercises and to enable digestion of the underlying concepts.
The concepts from asymptotic inference are crucial in modern statistics,but are difficult to grasp in view of their abstract nature. To overcome this difficulty,keeping up w.

The book presents the fundamental concepts from asymptotic statistical inference theory,elaborating on some basic large sample optimality properties of estimators and some test procedures. The most desirable property of consistency of an estimator and its large sample distribution,with suitable normalization,are discussed,the focus being on the consistent and asymptotically normal (CAN) estimators. It is shown that for the probability models belonging to an exponential family and a Cramer family,the maximum likelihood estimators of the indexing parameters are CAN. The book describes some large sample test procedures,in particular,the most frequently used likelihood ratio test procedure. Various applications of the likelihood ratio test procedure are addressed,when the underlying probability model is a multinomial distribution. These include tests for the goodness of fit and tests for contingency tables. The book also discusses a score test and Walds test,their relationship with the likelihood ratio test and Karl Pearsons chi-square test. An important finding is that,while testing any hypothesis about the parameters of a multinomial distribution,a score test statistic and Karl Pearsons chi-square test statistic are identical. Numerous illustrative examples of differing difficulty level are incorporated to clarify the concepts. For better assimilation of the notions,various exercises are included in each chapter. Solutions to almost all the exercises are given in the last chapter,to motivate students towards solving these exercises and to enable digestion of the underlying concepts.
The concepts from asymptotic inference are crucial in modern statistics,but are difficult to grasp in view of their abstract nature. To overcome this difficulty,keeping up w.

The book presents the fundamental concepts from asymptotic statistical inference theory,elaborating on some basic large sample optimality properties of estimators and some test procedures. The most desirable property of consistency of an estimator and its large sample distribution,with suitable normalization,are discussed,the focus being on the consistent and asymptotically normal (CAN) estimators. It is shown that for the probability models belonging to an exponential family and a Cramer family,the maximum likelihood estimators of the indexing parameters are CAN. The book describes some large sample test procedures,in particular,the most frequently used likelihood ratio test procedure. Various applications of the likelihood ratio test procedure are addressed,when the underlying probability model is a multinomial distribution. These include tests for the goodness of fit and tests for contingency tables. The book also discusses a score test and Walds test,their relationship with the likelihood ratio test and Karl Pearsons chi-square test. An important finding is that,while testing any hypothesis about the parameters of a multinomial distribution,a score test statistic and Karl Pearsons chi-square test statistic are identical. Numerous illustrative examples of differing difficulty level are incorporated to clarify the concepts. For better assimilation of the notions,various exercises are included in each chapter. Solutions to almost all the exercises are given in the last chapter,to motivate students towards solving these exercises and to enable digestion of the underlying concepts.
The concepts from asymptotic inference are crucial in modern statistics,but are difficult to grasp in view of their abstract nature. To overcome this difficulty,keeping up w.

The book presents the fundamental concepts from asymptotic statistical inference theory,elaborating on some basic large sample optimality properties of estimators and some test procedures. The most desirable property of consistency of an estimator and its large sample distribution,with suitable normalization,are discussed,the focus being on the consistent and asymptotically normal (CAN) estimators. It is shown that for the probability models belonging to an exponential family and a Cramer family,the maximum likelihood estimators of the indexing parameters are CAN. The book describes some large sample test procedures,in particular,the most frequently used likelihood ratio test procedure. Various applications of the likelihood ratio test procedure are addressed,when the underlying probability model is a multinomial distribution. These include tests for the goodness of fit and tests for contingency tables. The book also discusses a score test and Walds test,their relationship with the likelihood ratio test and Karl Pearsons chi-square test. An important finding is that,while testing any hypothesis about the parameters of a multinomial distribution,a score test statistic and Karl Pearsons chi-square test statistic are identical. Numerous illustrative examples of differing difficulty level are incorporated to clarify the concepts. For better assimilation of the notions,various exercises are included in each chapter. Solutions to almost all the exercises are given in the last chapter,to motivate students towards solving these exercises and to enable digestion of the underlying concepts.
The concepts from asymptotic inference are crucial in modern statistics,but are difficult to grasp in view of their abstract nature. To overcome this difficulty,keeping up w.

The book presents the fundamental concepts from asymptotic statistical inference theory,elaborating on some basic large sample optimality properties of estimators and some test procedures. The most desirable property of consistency of an estimator and its large sample distribution,with suitable normalization,are discussed,the focus being on the consistent and asymptotically normal (CAN) estimators. It is shown that for the probability models belonging to an exponential family and a Cramer family,the maximum likelihood estimators of the indexing parameters are CAN. The book describes some large sample test procedures,in particular,the most frequently used likelihood ratio test procedure. Various applications of the likelihood ratio test procedure are addressed,when the underlying probability model is a multinomial distribution. These include tests for the goodness of fit and tests for contingency tables. The book also discusses a score test and Walds test,their relationship with the likelihood ratio test and Karl Pearsons chi-square test. An important finding is that,while testing any hypothesis about the parameters of a multinomial distribution,a score test statistic and Karl Pearsons chi-square test statistic are identical. Numerous illustrative examples of differing difficulty level are incorporated to clarify the concepts. For better assimilation of the notions,various exercises are included in each chapter. Solutions to almost all the exercises are given in the last chapter,to motivate students towards solving these exercises and to enable digestion of the underlying concepts.
The concepts from asymptotic inference are crucial in modern statistics,but are difficult to grasp in view of their abstract nature. To overcome this difficulty,keeping up w.

The book presents the fundamental concepts from asymptotic statistical inference theory,elaborating on some basic large sample optimality properties of estimators and some test procedures. The most desirable property of consistency of an estimator and its large sample distribution,with suitable normalization,are discussed,the focus being on the consistent and asymptotically normal (CAN) estimators. It is shown that for the probability models belonging to an exponential family and a Cramer family,the maximum likelihood estimators of the indexing parameters are CAN. The book describes some large sample test procedures,in particular,the most frequently used likelihood ratio test procedure. Various applications of the likelihood ratio test procedure are addressed,when the underlying probability model is a multinomial distribution. These include tests for the goodness of fit and tests for contingency tables. The book also discusses a score test and Walds test,their relationship with the likelihood ratio test and Karl Pearsons chi-square test. An important finding is that,while testing any hypothesis about the parameters of a multinomial distribution,a score test statistic and Karl Pearsons chi-square test statistic are identical. Numerous illustrative examples of differing difficulty level are incorporated to clarify the concepts. For better assimilation of the notions,various exercises are included in each chapter. Solutions to almost all the exercises are given in the last chapter,to motivate students towards solving these exercises and to enable digestion of the underlying concepts.
The concepts from asymptotic inference are crucial in modern statistics,but are difficult to grasp in view of their abstract nature. To overcome this difficulty,keeping up w.

The book presents the fundamental concepts from asymptotic statistical inference theory,elaborating on some basic large sample optimality properties of estimators and some test procedures. The most desirable property of consistency of an estimator and its large sample distribution,with suitable normalization,are discussed,the focus being on the consistent and asymptotically normal (CAN) estimators. It is shown that for the probability models belonging to an exponential family and a Cramer family,the maximum likelihood estimators of the indexing parameters are CAN. The book describes some large sample test procedures,in particular,the most frequently used likelihood ratio test procedure. Various applications of the likelihood ratio test procedure are addressed,when the underlying probability model is a multinomial distribution. These include tests for the goodness of fit and tests for contingency tables. The book also discusses a score test and Walds test,their relationship with the likelihood ratio test and Karl Pearsons chi-square test. An important finding is that,while testing any hypothesis about the parameters of a multinomial distribution,a score test statistic and Karl Pearsons chi-square test statistic are identical. Numerous illustrative examples of differing difficulty level are incorporated to clarify the concepts. For better assimilation of the notions,various exercises are included in each chapter. Solutions to almost all the exercises are given in the last chapter,to motivate students towards solving these exercises and to enable digestion of the underlying concepts.
The concepts from asymptotic inference are crucial in modern statistics,but are difficult to grasp in view of their abstract nature. To overcome this difficulty,keeping up w.

The book presents the fundamental concepts from asymptotic statistical inference theory,elaborating on some basic large sample optimality properties of estimators and some test procedures. The most desirable property of consistency of an estimator and its large sample distribution,with suitable normalization,are discussed,the focus being on the consistent and asymptotically normal (CAN) estimators. It is shown that for the probability models belonging to an exponential family and a Cramer family,the maximum likelihood estimators of the indexing parameters are CAN. The book describes some large sample test procedures,in particular,the most frequently used likelihood ratio test procedure. Various applications of the likelihood ratio test procedure are addressed,when the underlying probability model is a multinomial distribution. These include tests for the goodness of fit and tests for contingency tables. The book also discusses a score test and Walds test,their relationship with the likelihood ratio test and Karl Pearsons chi-square test. An important finding is that,while testing any hypothesis about the parameters of a multinomial distribution,a score test statistic and Karl Pearsons chi-square test statistic are identical. Numerous illustrative examples of differing difficulty level are incorporated to clarify the concepts. For better assimilation of the notions,various exercises are included in each chapter. Solutions to almost all the exercises are given in the last chapter,to motivate students towards solving these exercises and to enable digestion of the underlying concepts.
The concepts from asymptotic inference are crucial in modern statistics,but are difficult to grasp in view of their abstract nature. To overcome this difficulty,keeping up w.

The book presents the fundamental concepts from asymptotic statistical inference theory,elaborating on some basic large sample optimality properties of estimators and some test procedures. The most desirable property of consistency of an estimator and its large sample distribution,with suitable normalization,are discussed,the focus being on the consistent and asymptotically normal (CAN) estimators. It is shown that for the probability models belonging to an exponential family and a Cramer family,the maximum likelihood estimators of the indexing parameters are CAN. The book describes some large sample test procedures,in particular,the most frequently used likelihood ratio test procedure. Various applications of the likelihood ratio test procedure are addressed,when the underlying probability model is a multinomial distribution. These include tests for the goodness of fit and tests for contingency tables. The book also discusses a score test and Walds test,their relationship with the likelihood ratio test and Karl Pearsons chi-square test. An important finding is that,while testing any hypothesis about the parameters of a multinomial distribution,a score test statistic and Karl Pearsons chi-square test statistic are identical. Numerous illustrative examples of differing difficulty level are incorporated to clarify the concepts. For better assimilation of the notions,various exercises are included in each chapter. Solutions to almost all the exercises are given in the last chapter,to motivate students towards solving these exercises and to enable digestion of the underlying concepts.
The concepts from asymptotic inference are crucial in modern statistics,but are difficult to grasp in view of their abstract nature. To overcome this difficulty,keeping up w.

The book presents the fundamental concepts from asymptotic statistical inference theory,elaborating on some basic large sample optimality properties of estimators and some test procedures. The most desirable property of consistency of an estimator and its large sample distribution,with suitable normalization,are discussed,the focus being on the consistent and asymptotically normal (CAN) estimators. It is shown that for the probability models belonging to an exponential family and a Cramer family,the maximum likelihood estimators of the indexing parameters are CAN. The book describes some large sample test procedures,in particular,the most frequently used likelihood ratio test procedure. Various applications of the likelihood ratio test procedure are addressed,when the underlying probability model is a multinomial distribution. These include tests for the goodness of fit and tests for contingency tables. The book also discusses a score test and Walds test,their relationship with the likelihood ratio test and Karl Pearsons chi-square test. An important finding is that,while testing any hypothesis about the parameters of a multinomial distribution,a score test statistic and Karl Pearsons chi-square test statistic are identical. Numerous illustrative examples of differing difficulty level are incorporated to clarify the concepts. For better assimilation of the notions,various exercises are included in each chapter. Solutions to almost all the exercises are given in the last chapter,to motivate students towards solving these exercises and to enable digestion of the underlying concepts.
The concepts from asymptotic inference are crucial in modern statistics,but are difficult to grasp in view of their abstract nature. To overcome this difficulty,keeping up w.

The book presents the fundamental concepts from asymptotic statistical inference theory,elaborating on some basic large sample optimality properties of estimators and some test procedures. The most desirable property of consistency of an estimator and its large sample distribution,with suitable normalization,are discussed,the focus being on the consistent and asymptotically normal (CAN) estimators. It is shown that for the probability models belonging to an exponential family and a Cramer family,the maximum likelihood estimators of the indexing parameters are CAN. The book describes some large sample test procedures,in particular,the most frequently used likelihood ratio test procedure. Various applications of the likelihood ratio test procedure are addressed,when the underlying probability model is a multinomial distribution. These include tests for the goodness of fit and tests for contingency tables. The book also discusses a score test and Walds test,their relationship with the likelihood ratio test and Karl Pearsons chi-square test. An important finding is that,while testing any hypothesis about the parameters of a multinomial distribution,a score test statistic and Karl Pearsons chi-square test statistic are identical. Numerous illustrative examples of differing difficulty level are incorporated to clarify the concepts. For better assimilation of the notions,various exercises are included in each chapter. Solutions to almost all the exercises are given in the last chapter,to motivate students towards solving these exercises and to enable digestion of the underlying concepts.
The concepts from asymptotic inference are crucial in modern statistics,but are difficult to grasp in view of their abstract nature. To overcome this difficulty,keeping up w.

Weight: 934g
Dimension: 166 x 242 x 37 (mm)
ISBN-13: 9789811590023
Edition number: 1st ed. 2021